0000000000660770
AUTHOR
Cristina Turrini
The varieties of bifocal Grassmann tensors
AbstractGrassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a pair of projections from a projective space onto view spaces of varying dimensions, generalize the classical notion of fundamental matrices. In this paper, we study in full generality the variety of bifocal Grassmann tensors focusing on its birational geometry. To carry out this analysis, every object of multi-view geometry is described both from an algebraic and geometric point of view, e.g., the duality between the view spaces, and the space of rays is explicitly described via polarity. Next, we deal with the moduli of bifocal Grassmann…
The Rank of Trifocal Grassmann Tensors
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerat…